Sets



In this homepage we have stored several pointsets suitable for interpolation or cubature on intervals, simplex (triangle), square, disk and polygons.

INTERVAL:
  1. General set with low Lebesgue constant: [.m]
  2. Extended Chebyshev: [.m]
  3. Gauss-Legendre-Lobatto (Fekete points in the interval): [.m]

SIMPLEX (TRIANGLE):
  1. General set with low Lebesgue constant: [.m] (last update: Jan 08, 2017, old version: [.m]).
  2. General set with low Lebesgue constant and Gauss-Legendre-Lobatto distribution on the side: [.m]
  3. General set with high absolute value of the Vandermonde matrix, i.e. (quasi-) Fekete points: [.m]
  4. Symmetric set with low Lebesgue constant: [.m]
  5. Weakly Admissible Mesh: [.m]
  6. Best cubature sets on the triangle (up to degree 50): [.m]
  • For a comparison on several interpolation sets see also: [html].
  • For a comparison on several cubature sets see also: [html].
  • You may find useful the M-file for the evaluation of the Vandermonde matrix w.r.t. Dubiner Legendre basis [.m] as orthonormal basis and [.m] as orthogonal basis with its derivatives (in a form suitable for cubature, i.e. it is the transpose of the Vandermonde matrix for interpolation purposes).

SQUARE:
  1. General set with low Lebesgue constant: [.m] (last update: Jan 08, 2017, old version: [.m]).
  2. General set with high absolute value of the Vandermonde matrix, i.e. (quasi-) Fekete points: [.m]
  3. Padua-Jacobi points with low Lebesgue constant: [.m]
  4. Padua-Jacobi points with high absolute value of the Vandermonde matrix: [.m]
  5. Padua points: [.m]
  6. Almost minimal rules on the square (Legendre weight): [.m]

DISK:
  1. Good interpolation sets on the unit disk [.html]
  2. Weakly Admissible Mesh: [.m]
  • You may find useful the M-file for the evaluation of the Vandermonde matrix w.r.t. Koornwinder II basis: [.m]

POLYGONS:
  1. Weakly Admissible Mesh (Matlab program for its construction, via triangulation): [.zip]
  2. Weakly Admissible Mesh (Matlab program for its construction, via quadrangulation): [.zip]
  3. Polygauss, cubature rule (Matlab program for its construction): [.zip]